On Lie Symmetry Analysis of Certain Coupled Fractional Ordinary Differential Equations
- 10.2991/jnmp.k.210315.001How to use a DOI?
- System of fractional ODEs; Lie group formalism; Laplace transform technique; Mittag-Leffler function; Exact solution
In this article, we explain how to extend the Lie symmetry analysis method for n-coupled system of fractional ordinary differential equations in the sense of Riemann-Liouville fractional derivative. Also, we systematically investigated how to derive Lie point symmetries of scalar and coupled fractional ordinary differential equations namely (i) fractional Thomas-Fermi equation, (ii) Bagley-Torvik equation, (iii) two-coupled system of fractional quartic oscillator, (iv) fractional type coupled equation of motion and (v) fractional Lotka-Volterra ABC system.The dimensions of the symmetry algebras for the Bagley-Torvik equation and its various cases are greater than 2 and for this reason we construct optimal system of one-dimensional subalgebras. In addition, the exact solutions of the above mentioned fractional ordinary differential equations are explicitly derived wherever possible using the obtained symmetries.
- © 2021 The Authors. Published by Atlantis Press B.V.
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- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
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TY - JOUR AU - K. Sethukumarasamy AU - P. Vijayaraju AU - P. Prakash PY - 2021 DA - 2021/03/31 TI - On Lie Symmetry Analysis of Certain Coupled Fractional Ordinary Differential Equations JO - Journal of Nonlinear Mathematical Physics SP - 219 EP - 241 VL - 28 IS - 2 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.k.210315.001 DO - 10.2991/jnmp.k.210315.001 ID - Sethukumarasamy2021 ER -